There are many different voting rules that could be used to elect a public official such as a president. Plurality rule (first-past-the-post), majority rule (Condorcet’s method), rank-order voting (Borda count), and runoff voting are just a few of the rules that have been used practically and studied theoretically.

One way to decide which rule is “best” is to proceed axiomatically. We can specify a set of desiderata (axioms) that we would like a voting rule to satisfy and then determine which rule(s) come closest to satisfying them.

Unfortunately, the best-known result in the voting literature is negative: the Gibbard-Satterthwaite theorem implies that there is no voting rule that always satisfies the following axioms: Pareto efficiency, anonymity (all voters should be treated equally), neutrality (all candidates should be treated equally), decisiveness (there should be a clear-cut winner), independence of irrelevant alternatives (the election outcome should be insensitive to removing marginal candidates from the ballot), and strategy-proofness (there should be no incentive to vote strategically, i.e., to vote for candidate A even though one prefers B). We show, however, that there is a sense in which majority rule satisfies these axioms more often than any other. If we drop the independence axiom, then majority rule and rank-order voting jointly satisfy the axioms the most often.